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Many U.S. National Parks have permit systems in place for commercial photographers, but typically they allow unrestricted or less restricted amateur photography (1,
2,3,4,5,6). Restrictions that sometimes apply include forbidding use of tripods or use of flash or use of anything. For example, link 3 says,

TRIPOD USAGE WITHIN RESTRICTED AREAS IS STRICTLY PROHIBITED WITH OR WITHOUT A PERMIT.
...
Lincoln Memorial: Filming/photography is prohibited above the white marble steps and the interior chamber of the Lincoln Memorial.
...
Washington Monument: Filming/photography is prohibited within the circle of flags surrounding the base of the Washington Monument. ...
Vietnam Veterans Memorial: Equipment set-up of any kind is prohibited at the Vietnam Veterans Memorial...

Generally, photography in National Parks that is intended to produce commercial photographs must be permitted in advance. Here is an excerpt from link 4 for the Great Sand Dunes National Park and Preserve, in the San Luis Valley of Colorado, that is typical of the language used for several different parks:

A permit is required for any commercial filming. Commercial filming is defined as digital or film recording
of a visual image or sound recording by a person, business, or other entity for a market audience, such as
for a documentary, television or feature film, advertisement, or similar project. Under P.L. 106-206 all
commercial filming requires a permit and is subject to a location fee and cost recovery.

You can publish without restriction pictures you take yourself in the parks, if they do not include persons who are recognizable. If persons are recognizable a model release is needed. For pictures taken by other people, copyright remains with the photographer unless other arrangements have been made (7).

A so-called “property release” is the kind of release used for pets (8,9).